Can't select vertices of different meshes in edit mode
Distinct objects can't share faces. If you're using blender versions before the (currently Beta) v.2.80 they can't even be edited simultaneously in Edit Mode.

If you need to make two meshes a single object, in order to be able to bridge vertices belonging to both of them, then in Object Mode select both and Join Meshes (CtrlJ). Then Edit the newly created joint object.